The combined quantum mechanics/molecular mechanics (QM/MM) and the ab initio molecular dynamics methods (AIMD) are fast emerging as viable computational molecular modeling tools. Both methods allow for the incorporation of effects that are often ignored in high level calculations, but may be critical to the real chemistry of the simulated system. In the combined QM/MM method part of the system, say the active site, is treated quantum mechanically whereas the remainder of the system is treated with a faster molecular mechanics force field. This allows high level calculations to be performed where the effects of the environment are incorporated in a computationally tractable manner. With the ab initio molecular dynamics methods, the system is simulated at a finite temperature with no empirical force field. Rather, the forces at each time step are determined with a full electronic structure calculation at the density functional level. Thus, simulations of chemical reactions can be performed where finite temperature effects are realistically represented. In this paper a brief introduction to both methods is given. The methods are further demonstrated with specific applications to modeling homogenous catalytic processes at the molecular level. These applications are our latest efforts to build more realistic computational models of catalytic systems at the density functional level.